A technique called a particle method is used in continuum motion analysis. The continuum motion analysis includes fluid analysis for examining the flow of fluid such as water and air by using numerical calculations, elastic body analysis for examining the behavior of a compressed elastic body such as rubber, and the like. A continuum is a set of mass points having macroscopic properties of the material, and the mass points are continuously and densely distributed in the space where the material exists. The particle method is a technique that represents a continuum by a distribution of particles and analyzes the motion of the continuum as the motion of particles. Known particle methods include a smoothed particle hydrodynamics (SPH) method and a moving particle semi-implicit (MPS) method. Further, there is a method called a distinct element method, which is a technique for representing the behavior of powder fluid based on the particle method.
When representing an object to be analyzed by a distribution of particles, a fixed boundary is set. There are various methods for representing a fixed boundary.
The following three methods are the typical methods for representing a fixed boundary based on the particle method. The first method disposes virtual fluid particles (hereinafter referred to as “boundary particles”) along a boundary, considers the boundary particles as fluid adhering to a fixed boundary, and thereby represents the fixed boundary. The second method sets a repulsive force between two particles, one being a boundary particle disposed in the same manner as the first method and the other one representing a continuum to be analyzed. The repulsive force has a magnitude as a function of the distance between the two particles, and has a direction along a relative position vector of the two particles. Thus, the area of motion of the particle representing the continuum is restricted to the inside of a fixed boundary. The third method disposes virtual continuum particles at positions that are reflectively symmetrical to the positions of particles representing a continuum to be analyzed, across a predetermined boundary surface, and thereby represents a fixed boundary.
Another method for representing a fixed boundary is to dispose boundary particles, apply a repulsive force in the normal direction of the boundary surface to a continuum particle that has approached any of the boundary particles within a certain distance, and thereby represent a fixed boundary.
There is also a method that represents a fixed boundary as a set of polygons. This method applies, between a continuum particle and a polygon whose coordinates of the center of gravity are closest to the continuum particle, a repulsive force based on the distance between the continuum particle and a plane containing the polygon. The repulsive force is applied only when the distance between the continuum particle and the plane containing the polygon is equal to or less than a certain value.
Further, there has been proposed a high versatile fluid analysis apparatus capable of uniformly handling a wettability model, and capable of accurately performing an analysis even with a low spatial resolution. The fluid analysis apparatus records the velocity, the position, and the pressure, for each of first particles representing fluid and for each of second particles representing a wall in contact with the fluid. Further, the fluid analysis apparatus specifies a contact angle θ between the fluid and the wall, and specifies a particle located within the range of application of an acting force to each particle from another particle. The fluid analysis apparatus calculates the acting force applied from the first particle using a first function, and calculates the acting force applied from the second particle using the first function multiplied by (1+cos θ)/2.
Further, there has been proposed a continuum motion analysis program that causes a computer to execute the following process. According to the continuum motion analysis program, the computer represents a continuum as particles, represents a fixed boundary as a set of micro regions (micro-surface elements) having an arbitrary shape, and calculates a repulsive force applied from each micro-surface element located within the influence range of each continuum particle to the continuum particle in the normal direction of the micro-surface element. Then, the computer calculates a force applied from the fixed boundary to the continuum particle by adding up the repulsive forces.
There has also been proposed a flow analysis method that is capable of handling an arbitrary shape with regard to the boundary condition on a fixed wall while reducing the calculation cost, and that has high calculation accuracy. According to the flow analysis method, for each of first particles determined to be within a predetermined distance from a wall boundary, the curvature of the wall boundary at the position closest to that first particle is calculated. Then, a plurality of second particles representing a wall are arranged as a boundary condition so as to be symmetrical to the first particles across the wall boundary while being enlarged with enlargement factors corresponding to the calculated curvatures.
See, for example, the following references:    Japanese Laid-open Patent Publication No. 2008-111675;    International Publication Pamphlet No. WO2012/025995;    Japanese Laid-open Patent Publication No. 2010-243293;    G. R. Liu, and M. B. Liu, “Smoothed Particle Hydrodynamics: A Meshfree Particle Method”, World Scientific Pub Co Inc., October 2003, pp. 138-141;    M. G. Gesteira, B. D. Rogers, R. A. Dalrymplem, A. J. C. Crespo, and M. Narayanaswamy, “User Guide for the SPHysics Code v1.4”, February 2009, pp. 16-19; and    Takahiro HARADA, Seiichi KOSHIZUKA, and Yoichiro KAWAGUCHI, “Real-time Fluid Simulation Coupled with Cloth” Proceedings of Information Processing Society of Japan, Proceedings of Graphics and CAD Research Society, Nov. 12, 2007, pp. 13-18.
Of these conventional techniques, the fixed-boundary representation method that represents the boundary surface as a set of micro-surface elements is capable of reducing the memory usage for analysis and the calculation time for analysis, and has fewer restrictions on the applicable situations, compared to other representation methods. However, this method applies a repulsive force to a continuum particle that has approached within a certain distance from any of the micro-surface elements, and therefore it is not possible to analyze the motion of a continuum in a region having a gap narrower than the certain distance. The distance from a boundary element in which repulsive force is applied is often set to be comparable to the average particle interval in accordance with the spatial resolution in numerical calculations, for example. Thus, when the particle interval is about 1 cm, it is not possible to handle the process of particles entering a gap with a width of about 5 mm.